JEE Main 2024 Mathematics question
Let α ∈ (0, ∞) and . If det(adj(2A − Aᵀ) · adj(A − 2Aᵀ)) = 2⁸, then (det(A))² is equal to-
Answer: (C)
Solution
det = [det(2A − Aᵀ) · det(A − 2Aᵀ)]² = (3α + 1)⁴ ⇒ (3α + 1)⁴ = 2⁸ ⇒ α = 1. Then det A = −4
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